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Computer Science Clay
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14-06-2009, 01:29 AM

Seminar Report On
Submitted by
In the partial fulfillment of requirements in degree of
Master of Technology in Computer and Information Science
2008Page 2

Apart from the efforts of me, the success of this seminar and presentation depends largely on the
encouragement and guidelines of many others.
I take this opportunity to express my gratitude to the people who have been
instrumental in the successful completion of this seminar and presentation.
First I thank Allah almighty for guiding me throughout this seminar and presentation and
then my teachers.
I am extremely grateful to Prof. Dr. K Poulose Jacob, Director, Department of
computer Science, for providing me with best facilitiesand atmosphere for the
creative work guidance and encouragement.
I would like to thank my coordinator, Mr. G. Santhosh Kumar for all help and
support extend to me I cants thank this person I appreciate his very much.
I thank all staff members of my college and friends for extending their
cooperationduringmy seminar and presentation.
Above all I would like to thank my parents without whose blessings; I would
not have been able to accomplish my goal.Page 3

The brain is a network of nerve cells connected by axons, and cells themselves
are networks of molecules connected by biochemical reactions.
Societies, too, are networks of people linked by friendships, familial relationships
and professional ties.
On a larger scale, food webs and ecosystems can be represented as networks of
And networks pervade technology: the Internet, power grids and transportation
systems are but a few examples.
Even the language we are using to convey these thoughts to you is a network,
made up of words connected by syntactic relationships.
Yet despite the importance and pervasiveness of networks, scientists have had
little understanding of their structure and properties.
Additional Key Words and Phrases: Scale, Free, Networks, Random.Page 4

1. INTROUDUCTION-----------------------------------------------------
2. SCALE-FREE NETWORK--------------------------------------------
2.1. Networks with out Scale------------------------------------------
2.3 Scale-Free Networks Abound------------------------------------
3. The Rich Get Richer-------------------------------------------------- 10
3.1 BIRTH OF ASCALE-FREE NETWORK---------------------------
3.1.1. An Achilles ' heel------------------------------------------------- 13
3.1.2. Scale-Free Epidemics------------------------------------------- 14
3.3. From Theory to Practice------------------------------------------ 18
4. Example of scale-free network ------------------------------------ 20
4.1. Disadvantage-------------------------------------------------------- 20
4.2. Applications----------------------------------------------------------
5. Conclusion------------------------------------------------------------
6. References-------------------------------------------------------------- 21Page 5

How do the interactions of several malfunctioning nodes in a complex genetic
network result in cancer? How does diffusion occur so rapidly?
In certain social and communications systems, leading to epidemics of diseases
and computer viruses?
How do some networks continue to function even after the vast majority of their
nodes have failed? Recent research has begun to answer such questions.
Over the past few years, investigators from a variety of fields have discovered
that many networks-from the World Wide Web to a cell's metabolic system to
actors in Hollywood-are dominated by a relatively small number of nodes that
are connected to many other sites.
Networks containing such important nodes, or hubs, tend to be what we call
"scale-free," in the sense that some hubs have a seemingly unlimited number of
links and no node is typical of the others.
These networks also behave in certain predictable ways; for example, they are
remarkably resistant to accidental failures but extremely vulnerable to
coordinated attacks. Such discoveries have dramatically changed what we
thought we knew about the complex interconnected world around us.
Unexplained by previous network theories, hubs offer convincing proof that
various complex systems have a strict architecture, ruled by fundamental laws,
laws that appear to apply equally to cells, computers, languages and society.
Furthermore, these organizing principles have significant implications for
developing better drugs, defending the Internet from hackers, and halting the
spread of deadly epidemics, among other applications.
2.1. Networks with out Scale
FOR MORE THAN 40 YEARS, science treated all complex networks as being
completely random. This paradigm has its roots in the work of two Hungarian
mathematicians, the inimitable Paul Erdos and his close collaborator Alfréd
Rényi.Page 6

In 1959, aiming to describe networks seen in communications and the life
sciences, Erdos and Rényi suggested that such systems could be effectively
modeled by connecting their nodes with randomly placed links.
The simplicity of their approach and the elegance of some of their related
theorems revitalized graph theory, leading to the emergence of a field in
mathematics that focuses on random networks.
An important prediction of random network theory is that, despite the random
placement of links, the resulting system will be deeply democratic: most nodes
will have approximately the same number of links.
Indeed, in a random network the nodes follow a Poisson distribution with a bell
shape, and it is extremely rare to find nodes that have significantly more or fewer
links than the average.
Random networks are also called exponential, because the probability that a
node is connected to k other sites decreases exponentially for large k.
So in 1998, when we, together with Hawoong Jeong and Réka Albert of the
University of Notre Dame, embarked on a project and implimentation to map the World Wide Web,
we expected to find a random network.
Here's why: people follow their unique interests when deciding what sites to link
their Web documents to, and given the diversity of everyone's interests and the
tremendous number of pages they can choose from, the resulting pattern of
connections should appear fairly random.
The measurements, however, defied that expectation. Software designed for this
project and implimentation hopped from one Web page to another and collected all the links it could.
Although this virtual robot reached only a tiny fraction of the entire Web, the
map it assembled revealed something quite surprising: a few highly connected
pages are essentially holding the World Wide Web together.
More than 80 percent of the pages on the map had fewer than four links, but a
small minority, less than 0.01 percent of all nodes, had more than 1,000. (A
subsequent Web survey would uncover one document that had been referenced
by more than two million other pages!)
Counting how many Web pages have exactly k links showed that the distribution
followed a so-called power law: the probability that any node was connected to k
other nodes was proportional to 1/ (k^n). The value of n for incoming links was
approximately 2, so, for instance, any node was roughly four times as likely to
have just half the number of incoming links as another node. Power laws are
quite different from the bell shaped distributions that characterize random
networks.Page 7

RANDOM NETWORK which resemble the U.S. highway system (simplified in left
map), consist of nodes with randomly placed connections. In such systems, a plot
of the distribution of node linkages will follow a bell-shaped curve (left graph),
with most nodes having approximately the same number of links. In contrast,
scale-free networks, which resemble, the U.S. airline system (simplified in right
map). Contain hubs [red)-nodes with a very high number of links. In such
networks, the distribution of node linkages follows a power law [center graph] in
that most nodes have just a few connections and some have a tremendous
number of links. In that sense, the system has no "scale."
The defining characteristic of such networks is that the distribution of links, if
plotted on a double-logarithmic scale
[right graph], results in a straight line.
See figure (1).
Figure (1)
Specifically, a power law does not have a peak, as a bell curve does, but is
instead described by a continuously decreasing function.
When plotted on a double-logarithmic scale, a power law is a straight line
[see illustration above]. In contrast to the democratic distribution of links seen in
random networks, power laws describe systems in which a few hubs, such as
Yahoo and Google, dominate.Page 8

Hubs are simply forbidden in random networks. When we began to map
the Web, we expected the nodes to follow a bell-shaped distribution, as do
people's heights. Instead we discovered certain nodes that defied explanation,
almost as if we had stumbled on a significant number of people who were 100
feet tall, thus prompting us to coin the term" scale-free."
2.3. Scale-Free Networks Abound
OVER THE PAST several years, researchers have uncovered scale free structures
in a stunning range of systems. When we studied the World Wide Web, we
looked at the virtual network of Web pages connected to one another by hyper
In contrast Michalis Faloutsos of the University of California at River side, Petros
Faloutsos of the University of Toronto and Christos Faloutsos of Carnegie Mellon
University analyzed the physical structure of the Internet.
These three computer-scientist brothers investigated the routers connected by
optical or other communications lines and found that the topology of that
network, too, is scale-free.
Researchers have also discovered that some social networks are scale-free.
A collaboration between scientists from Boston University and Stockholm
University, for instance, has shown that a network of sexual relationships among
people in Sweden followed a power law although most individuals had only a
few sexual partners during their lifetime, a few (the hubs) had hundreds.
A recent study led by Stefan Bornholdt of the University of Kiel in Germany
concluded that the network of people connected by e-mail is likewise scale free.
Sidney Redner of Boston University demonstrated that the network of scientific
papers, connected by citations, follows a power law as well.
And Mark Newman of the University of Michigan at Ann Arbor examined
collaborations among scientists in several disciplines, including physicians and
computer scientists, and found that those networks were also scale-free,
corroborating a study we conducted focusing on mathematicians and
(Interestingly, one of the largest hubs in the mathematics community is Erdos
himself, who wrote more than 1,400 papers with no fewer than 500 co-
authors).Scale-free networks can occur in business.
Walter W. Powell of Stanford University, Douglas R. White of the University of
at Irvine, Kenneth W. Koput of the University of Arizona, and Jason-Owen Smith
6f the University of Michigan studied the formation of alliance networks in the
U.S. biotechnology industry and discovered definite hubs for instance, companies
such as Genzyme, Chiron and Genentech had a disproportionately large number
of partnerships with other firms.Page 9

Researchers in Italy took a deeper look at that network.
Using data collected by the University of Siena's Pharmaceutical Industry
Database, which now provides information for around 20,100 R&D agreements
among more than 7,200 organizations, they found that the hubs detected by
Powell and his colleagues were actually part of a scale-free network.
Even the network of actors in Hollywood - popularized by the game Six Degrees
of Kevin Bacon, in which players try to connect actors to Bacon via the movies in
which they have appeared together- is scale-free.
A quantitative analysis of that network showed that it, too, is dominated by hubs.
Specifically, although most actors have only a few links to others, a handful of
actors, including Rod Steiger and Donald Pleasence, have thousands of
(Incidentally, on a list of most connected actors, Bacon ranked just 876th).
On a more serious note, scale-free networks are present in the biological realm.
With Zoltán Oltvai, a cell biologist from Northwestern
University, we found a scale-free structure in the cellular metabolic networks of
43 different organisms from all three domains of life, including Archaeoglobus
fulgidus (an archaebacterium), Escherichia coli (a eubacterium) and
Caenorhabditis elegans (a eukaryote).
In such networks, cells burn food by splitting complex molecules to release
Each node is a particular molecule, and each link is a biochemical reaction. We
found that most molecules participate in just one or two reactions, but a few (the
hubs), such as water and adenosine tri-phosphate, play a role in most of them.
We discovered that the protein-interaction network of cells is scale-free as well.
In such a network, two proteins are "connected" if they are known to interact
with each other.
When we investigated Baker's yeast, one of the simplest eukaryotic (nucleus-
containing) cells, with thousands of proteins, we discovered a scale-free topology
although most proteins interact with only one or two others; a few are able to
attach themselves physically to a huge number.
We found a similar result in the protein-interaction network of an organism that
is very different from yeast, a simple bacterium called Helicobacter pylori.
Indeed, the more that scientists studied networks, the more they uncovered
scale-free structures.
These findings raised an important question: How can systems as fundamentally
different as the cell and the Internet have the same architecture and obey the
same laws?Page 10

Not only are these various networks scale-free, they also share an intriguing
property: for reasons not yet known, the value of n in the ( k^n) term of the
power law tends to fall between 2 and 3.
3.The Rich Get Richer
PERHAPS a more basic question is why random-network theory fails to explain
the existence of hubs.
A closer examination of the work of Erdos and Renyi reveals two reasons. In
developing their model, Erdos and Rényi assumed that they had the full
inventory of nodes before they placed the links.
In contrast, the number of documents on the Web is anything but constant. In
1990 the Web had only one page.
Now it has more than three billion. Most networks have expanded similarly.
Hollywood had only a handful of actors in 1890, but as new people joined the
trade, the network grew to include more than half a million, with the rookies
connecting to veteran actors.
The Internet had only a few routers about three decades ago, but it gradually
grew to have millions, with the new routers always linking to those that were
already part of the network.
Thanks to the growing nature of real networks, older nodes had greater
opportunities to acquire links. Furthermore, all nodes are not equal.
When deciding where to link their Web page, people can choose from a few
billion locations. Yet most of us are familiar with only a tiny fraction of the full
Web, and that subset tends to include the more connected sites because they are
easier to find.
By simply linking to those nodes, people exercise and reinforce a bias toward
them. This process of "preferential attachment" occurs elsewhere.
In Hollywood the more connected actors are more likely to be chosen for new
roles. On the Internet the more connected routers, which typically have greater
bandwidth, are more desirable for new users.
In the U.S. biotech industry, well-established companies such as Genzyme tend to
attract more alliances, which further increases their desirability for future
Likewise, the most cited articles in the scientific literature stimulate even more
researchers to read and cite them, a phenomenon that noted sociologist Robert
K. Merton called the Matthew effect, after a passage in the New Testament: "For
unto every one that hath shall be given, and he shall have abundance."Page 11

These two mechanisms-growth and preferential attachment-help to explain the
existence of hubs: as new nodes appear, they tend to connect to the more
connected sites, and these popular locations thus acquire more links over time
than their less connected neighbors.
And this "rich get richer" process will generally favor the early nodes, which are
more likely to eventually become hubs.
Along with Reka Albert, we have used computer simulations and calculations to
show that a growing network with preferential attachment will indeed become
scale-free, with its distribution of nodes following a power law.
Although this theoretical model is simplistic and needs to be adapted to specific
situations, it does appear to confirm our explanation for why scale-free networks
are so ubiquitous in the real world.
Growth and preferential attachment can even help explicate the presence of
scale-free networks in biological systems.
Andreas Wagner of the University of New Mexico and David A. Fell of Oxford
Brookes University in England have found, for instance, that the most-connected
molecules in the E. coli metabolic network tend to have an early evolutionary
history: some are believed to be remnants of the so-called RNA world (the
evolutionary step before the emergence of DNA), and others are components of
the most ancient metabolic pathways.
Interestingly, the mechanism of preferential attachment tends to be linear.
In other words, a new node is twice as likely to link to an existing node that has
twice as many connections as its neighbor.
Redner and his colleagues at Boston University and elsewhere have investigated
different types of preferential attachment and have learned that if the
mechanism is faster than linear
(for example, a new node is four times as likely to link to an existing node that
has twice as many connections), one hub will tend to run away with the lion's
share of connections.
In such "winner take all" scenarios, the network eventually assumes a star
topology with a central hub.Page 12

A SCALE-FREENETWORK grows incrementally from two to 11 nodes in this
example. When deciding where to establish a link, a new node (green) prefers to
attach to an existing node (red) that already has many other connections.
These two basic mechanisms-growth and preferential attachment-will
eventually lead to the system's being dominated by hubs, nodes having an
enormous number of links.
See figure(2)
Figure(2)Page 13

3.1.1. An Achilles' Heel
AS HUMANITY BECOMES increasingly dependent on power grids and
communications webs, a much-voiced concern arises: Exactly how reliable are
these types of networks?
The good news is that complex systems can be amazingly resilient against
accidental failures.
In fact, although hundreds of routers routinely malfunction on the Internet at
any moment, the network rarely suffers major disruptions.
A similar degree of robustness characterizes. Living systems: people rarely
notice the consequences of thousands of errors in their cells, ranging from
mutations to misfolded proteins.
What is the origin of this robustness?
Intuition tells us that the breakdown of a substantial number of nodes will result
in a network's inevitable fragmentation. This is certainly true for random
networks: if a critical fraction of nodes is removed, these systems break into tiny,
non-communicating islands.
Yet simulations of scale-free networks tell a different story: as many as 80
percent of randomly selected Internet routers can fail and the remaining ones
will still form a compact cluster in which there will still be a path between any
two nodes.
It is equally difficult to disrupt a cell's protein-interaction network: our
measurements indicate that even after a high level of random mutations are
introduced; the unaffected proteins will continue to work together.
In general, scale-free networks display an amazing robustness against accidental
failures, a property that is rooted in their inhomogeneous topology.
The random removal of nodes will take out mainly the small ones because they
are much more plentiful than hubs.
And the elimination of small nodes will not disrupt the network topology
significantly, because they contain few links compared with the hubs, which
connect to nearly everything.
But a reliance on hubs has a serious drawback: vulnerability to attacks.
In a series of simulations, we found that the removal of just a few key hubs from
the Internet splintered the system into tiny groups of hopelessly isolated routers.
Similarly, knockout experiments in yeast have shown that the removal of the
more highly connected proteins has a significantly greater chance of killing the
organism than does the deletion of other nodes.Page 14

These hubs are crucial-if mutations make them dysfunctional, the cell will most
likely die.
A reliance on hubs can be advantageous or not, depending on the system.
Certainly, resistance to random breakdown is good news for both the Internet
and the cell. In addition, the cell's reliance on hubs provides pharmaceutical
researchers with new strategies for selecting drug targets, potentially leading to
cures that would kill only harmful cells or bacteria by selectively targeting their
hubs, while leaving healthy tissue unaffected.
But the ability of a small group of well-informed hackers to crash the entire
communications infrastructure by targeting its hubs is a major reason for
The Achilles' heel of scale-free networks raises a compelling question: How many
hubs are essential? Recent research suggests that, generally speaking, the
simultaneous elimination of as few as 5 to 15 percent of all hubs can crash a
For the Internet, our experiments imply that a highly coordinated attack-first
removing the largest hub, then the next largest, and so on-could cause significant
disruptions after the elimination of just several hubs.
Therefore, protecting the hubs is perhaps the most effective way to avoid large-
scale disruptions caused by malicious cyber-attacks
But much more work is required to determine just how fragile specific networks
For instance, could the failure of several hubs like Genzyme and Genentech lead
to the collapse of the entire U.S. biotech industry?
3.1.2Scale-Free Epidemics
KNOWLEDGE ABOUT scale-free networks has implications for understanding the
spread of computer viruses, diseases and fads.
Diffusion theories, intensively studied for decades by both epidemiologists and
marketing experts, predict a critical threshold for the propagation of a contagion
throughout a population.
Any virus, disease or fad that is less infectious than that well-defined threshold
will inevitably die out, whereas those above the threshold will multiply
exponentially, eventually penetrating the entire system.
Recently, though, Romualdo Pastor-Satorras of the Polytechnic University of
Catalonia in Barcelona and Alessandro Vespigniani of the International Center
for Theoretical Physics in Trieste, Italy, reached a disturbing conclusion.Page 15

They found that in a scale-free network the threshold is zero. That is, all viruses,
even those that are weakly contagious, will spread and persist in the system.
This result explains why Love Bug, the most damaging computer virus thus far
(it shut down the British Parliament in 2000), was still one of the most pervasive
viruses a year after its supposed eradication.
Because hubs are connected to many other nodes, at least one hub will tend to be
infected by any corrupted node.
And once a hub has been infected, it will pass the virus to numerous other sites,
eventually compromising other hubs, which will then spread the virus
throughout the entire system.
The fact that biological viruses spread in social networks, which in many cases
appear to be scale-free, suggests that scientists should take a second look at the
volumes of research written on the interplay of network topology and epidemics.
Specifically, in a scale-free network, the traditional public health approach of
random immunization could easily fail because it would very likely neglect a
number of the hubs.
In fact, nearly everyone would have to be treated to ensure that the hubs were
not missed.
A vaccination for measles, for instance, must reach 90 percent of the population
to be effective.
Instead of random immunizations, though, what if doctors targeted the hubs, or
the most connected individuals? Research in scale-free networks indicates that
this alternative approach could be effective even if the immunizations reached
only a small fraction of the overall population, provided that the fraction
contained the hubs.
But identifying the hubs in a social network is much more difficult than
detecting them in other types of systems. Nevertheless, Reuven Cohen and
Shlomo Havlin of Bar-Han University in Israel, together with Daniel ben-
Avraham of Clarkson University, have proposed a clever solution: immunize a
small fraction of the random acquaintances of arbitrarily selected individuals, a
procedure that selects hubs with a high probability because they are linked to
many people.Page 16

That approach, though, leads to a number of ethical dilemmas.
For instance, even if the hubs could be identified, should they have
priority for immunizations and cures?
Such issues notwithstanding, targeting hubs could be the most pragmatic
solution for the future distribution of AIDS or smallpox vaccines in countries and
regions that do not have the resources to treat everyone.
In many business contexts, people want to start, not stop, epidemics.
Viral marketing campaigns, for instance, often specifically try to target
hubs to speed the adoption of a product.
Obviously, such a strategy is not new. Back in the 1950s, a study funded
by pharmaceutical giant Pfizer discovered the important role that hubs play in
how quickly a community of doctors begins using a new drug.
Indeed, marketers have intuitively known for some time that certain
customers outshine others in spreading promotional buzz about products and
But recent work in scale-free networks provides the scientific framework
and mathematical tools to probe that phenomenon more rigorously.Page 17

THE ACCIDENTAL FAILURE of a number of nodes in a random network (top
panels) can fracture the system into non communicating islands.
In contrast, scale-free networks are more robust in the face of such failures
(middle panels).
But they are highly vulnerable to a coordinated attack against their hubs (bottom
See figure (3).
Figure (3)
.Page 18

3.3. From Theory to Practice
ALTHOUGH SCALE-FREE networks are pervasive, numerous prominent
exceptions exist.
For example, the highway system and power grid in the U.S. are not scale-free.
Neither are most networks seen in materials science.
In a crystal lattice, for instance, atoms have the same number of links to their
neighbors. With other networks, the data are inconclusive.
The relatively small size of food webs, which show predator-prey relationships,
has prevented scientists from reaching a clear conclusion regarding that
network's type.
And the absence of large-scale connectivity maps of the brain has kept
researchers from knowing the nature of that important network as well.
Determining whether a network is scale-free is important in understanding the
system's behavior, but other significant parameters merit attention, too.
One such characteristic is the diameter, or path length, of a network: the largest
number of hops required to get from one node to another by following the
shortest route possible.
Finally, knowledge of a network's general topology is just part of the story in
understanding the overall characteristics and behavior of such systems.
There might be steep costs, for instance, with the addition of each link to a given
node that could prevent certain networks (such as the U.S. highway system) from
becoming scale free.
In food chains, some preys are easier to catch than others, and that fact has a
profound effect on the overall ecosystem.
With social networks, ties among household members are much stronger than
connections to casual acquaintances, so diseases (and information) are more
likely to spread through such linkages.
For transportation, transmission and communications systems (such as the
Internet), congestion along specific links is a major consideration: too much
traffic on a particular link can cause it to break down, leading to the potential
failure of other links that must then handle the spillover.
And the nodes themselves might not be homogeneous-certain Web pages have
more interesting content, for instance which could greatly alter the preferential
attachment mechanism.Page 19

Because of these and other factors, scientists have only begun to uncover the
behavior of scale-free systems.
Immunizing hubs, for instance, might not be sufficient to stop the spread of a
disease; a more effective solution might be found by considering not just the
number of connections a person has but also the frequency and duration of
contact for those links.
In essence, we have studied complex networks first by ignoring the details of
their individual links and nodes.
By distancing ourselves from those particulars, we have been able to better
glimpse some of the organizing principles behind these seemingly
incomprehensible systems.
At the very least, knowledge from this endeavor has led to the rethinking of
many basic assumptions.
In the past, for example, researchers modeled the Internet as a random network
to test how a new routing protocol might affect system congestion. But we now
know that the Internet is a scale-free system with behavior that is dramatically
different from a random network's.
Consequently, investigators such as John W. Byers and his colleagues at Boston
University are revamping the computer models they have been using to simulate
the Internet.
Similarly, knowledge of the properties of scale-free networks will be valuable in
a number of other fields, especially as we move beyond network topologies to
probe the intricate and often subtle dynamics taking place within those complex
systems.Page 20

4.1. Disadvantage
Scale-free networks are vulnerable to spreading viruses.
--Hubs are passing them massively to the connected multiple nodes.
4.2. Applications
Social search / Network navigation.
--Decision making.
Mobile ad hoc networks
-Peer-to-peer networks.
-Page 21

5. Conclusion
Scale-free property is conserved via line graph transformation where
exponent is increased by 1.
Line graph transformation reproduces a peak which is found in many
experimental data for nodes of low degree.
6. References
[1] A. Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata, A.
Tomkins, and J. Wiener, Graph structure in the web, Computer Networks, 33
(2000), pp. 309“320; available from
[2] V. Latora and M. Marchiori, Economic Small-World Behavior in Weighted
Networks, Preprint 0204089 (2002); available
[3] Www://
[4] Http://en.wikipediawiki/Scale-free_network
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